Singular-perturbative reduction to Birkhoff normal form and instanton-type formal solutions of Hamiltonian systems

DOI10.2977/prims/1195144426zbMath0952.34075OpenAlexW2053620255MaRDI QIDQ1974506

Yoshitsugu Takei

Publication date: 28 December 2000

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195144426

zbMATH Keywords

Hamiltonian systemsBirkhoff normal formPainlevé equationsresidueregular singular pointinstanton-type formal solutionssingular-perturbative reduction

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Singular perturbations for ordinary differential equations (34E15) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

We Found 4 Related Items (max. 100)

Riccati equations revisited: linearization and analytic interpretation of instanton-type solutions ⋮ Instanton-type solutions for the second and the fourth Painlevé hierarchies with a large parameter ⋮ WKB analysis of higher order Painlevé equations with a large parameter -- local reduction of 0-parameter solutions for Painlevé hierarchies \((P_{J})\) (\(J=\text{ I, II-1 or II-2}\)) ⋮ On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painlevé equation

Cites Work

• Reduction for Painlevé equations at the fixed singular points of the second kind
• WKB analysis of Painlevé transcendents with a large parameter. III: Local reduction of 2-parameter Painlevé transcendents
• WKB analysis of Painlevé transcendents with a large parameter. I
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